Create PowerWithoutUsingMultiplicationAndDivisionOperators

Author: nkatre

MathematicalOperations/PowerWithoutUsingMultiplicationAndDivisionOperators

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+/*
+Write you own Power without using multiplication(*) and division(/) operators
+Source: http://www.geeksforgeeks.org/write-you-own-power-without-using-multiplication-and-division/
+*/
+package PowerWithoutUsingMultiplicationAndDivisionOperators;
+
+import java.util.Scanner;
+
+public class UsingRecursiveAddition {
+public static void main(String[] args) {
+	Scanner in = new Scanner(System.in);
+	try{
+		System.out.println("Enter the two number to calculate the power in the form a^b repectively");
+		System.out.println("Only positive numbers should be entered");
+		int a = in.nextInt();
+		int b = in.nextInt();
+		System.out.println("Using multiplcative recursion we get "+pow(a,b));
+		System.out.println("Using nested loops "+usingNestedLoops(a,b));
+	}
+	finally{
+		in.close();
+	}
+}
+/*
+Algorithm:
+	Method 1 - (Using Nested Loops)
+
+	We can calculate power by using repeated addition.
+
+	For example to calculate 5^6.
+	1) First 5 times add 5, we get 25. (5^2)
+	2) Then 5 times add 25, we get 125. (5^3)
+	3) Then 5 time add 125, we get 625 (5^4)
+	4) Then 5 times add 625, we get 3125 (5^5)
+	5) Then 5 times add 3125, we get 15625 (5^6)
+	
+	Method 2 - (Using Recursion)
+	Recursively add a to get the multiplication of two numbers. And recursively multiply to get a raise to the
+	power b.
+*/
+private static int usingNestedLoops(int a, int b) {
+	if(b==0)
+		return 1;
+	int increment = a;   // initialize increment with a
+	int result = a;      // initialize result with a
+	for(int i=1;i<b;i++){     // Hand Run this program to understand the logic
+		for(int j=1;j<a;j++){
+			result+=increment;
+		}
+		increment = result;
+	}
+	return result;
+}
+/*
+Analysis:
+	Time Complexity = O(a*b)
+	Space Complexity = O(1)	
+*/
+private static int pow(int a, int b) {
+	if(b==0)
+		return 1;
+	else
+		return mutiply(a,pow(a,b-1));  // multiplication of (a * pow(a,b-1))
+}
+
+private static int mutiply(int a, int b) {
+	if(b==0)
+		return 0;
+	else
+		return a+mutiply(a,b-1);
+}
+}
+/*
+Analysis:
+	Time Complexity = O(b^2)
+	Space Complexity = O(1) // This is not the space complexity
+	
+*/